A hypothesis test is conducted at the 5 percent level of sig

A hypothesis test is conducted at the 5 percent level of significance to test whether the population correlation is zero . If the sample consists of 25 observations and the correlation coefficient is 0.60, then the computed test statistic would be:

Solution

H0: Rho = 0 Ha : Rho not equal to 0 Rho is the population correlation coefficient. t = r sqrt [n-2] / sqrt [(1-r^2)] t = (0.60) sqrt [23] / (1- (0.6)^2) t = 3.597 This is compared with a critical t (23 degrees of freedom two-tailed value) = 2.069 Since computed t exceeds critical t, reject H0 and conclude the population correlation coefficient significantly differs from 0 at 5% level of significance.